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7/21/2019 Quimica de Materiales-1
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Equacion de Schrodinger
Hamiltoniano (Operador de energia total)
Funccion de ondaPrincipio de incertidumbre de Heisenberg
Fundamentos Basicos
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3-dimensiones
Sistema de n particulas
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sisi
Algebra de operadores
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Operadores de dierentes !ariables
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Operadores lineales
Operadores Hermitianos
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"alores esperados
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Principio de incertidumbre
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Hamiltoniano de un sistema polielectronico en aproma#icion de Born$ Openheimer
Apro#imacion de Born % Openheimer
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Particula en un po&o de Potencial
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Particula en un po&o de Potencial (continuacion)
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' (pm) heor% E#perimentc%anine * 3+, nm +3 nm
pinac%anol ,3 3 nm *. nm
dicarboc%anin
e
///+ ,. nm 0.* nm
Particula en un po&o de Potencial (aplicacion)
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Principio de Pauli
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Apro#imacion de Hartree-Foc1
Hamiltonian contains t2o terms that act
on one electron at a time the 1inetic
energ% and the electron-nucleus
attraction and a term that describes the
pair2ise repulsion o electrons4 he latterdepends on the coordinates o t2o
electrons at the same time
o a!oid this problem the
independent particle appro#imation is
introduced 5 the interaction o each
electron 2ith all the others is treated
in an a!erage 2a%4
hen the Schr6dinger equation 2hich initiall%
depended on the coordinates x (representing
spatial and spin coordinates) o all electrons
can be reduced to a set o equations
Spin orbital
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He atom
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7oopmans8 heorem
he Pauli principle states that the 2a!eunction must change sign
2hen t2o independent electronic coordinates are interchanged
For t2o electron s%stem
Slater determinant
P i i i i i l
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Principio !ariacional
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eoria de perturbacion independiente de tiempo
i d ti l d l d id d
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eoria de unctionales de la densidad
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Atomo de Hidrogeno % Atomos Polielectronicos
solucion
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Simetria de los orbitales
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999
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he Aubau Principal
: ;hen placing electrons into orbitals in theconstruction o pol%electronic atoms 2e use theAubau Principle4
: his principle states that in addition to adding protons and neutrons to the nucleus one simpl%adds electrons to the h%drogen-li1e atomic orbitals
: Pauli e#clusion principle5 <o t2o electrons ma%ha!e the same quantum numbers4 hereore onl%t2o electrons can reside in an orbital
(dierentiated b% ms)4
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he Aubau Principal (cont4)
: Finall% orbitals are illed starting rom the lo2estenerg%4
:E#ample5 H%drogen
1s 2s 2p
: E#ample5 Helium (= > +)
1s 2s 2p
1s1
1s2
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he Aubau Principal (cont4)
: 'ithium (= > 3)
1s 2s 2p
1s 2s 2p
: Berillium (= > )
: Boron (= > )
1s 2s 2p
1s22s1
1s22s2
1s22s22p1
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he Aubau Principal (cont4)
: ?arbon (= > *)
1s 2s 2p
1s 2s 2p
: <itrogen (= > 0)
Hund’s Rule: Lowest energy configuration is
the one in which the maximum number of unpaired electrons
are distributed amongst a set of degenerate orbitals.
1s22s22p2
1s22s22p3
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he Aubau Principal (cont4)
: O#%gen (= > ,)
1s 2s 2p
1s 2s 2p
: Fluorine (= > @)
1s22s22p4
1s22s22p5
1s 2s 2p
: <eon (= > /.)
1s22s22p6
full
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he Aubau Principal (cont4)
: Sodium (= > //)
3s
1s22s22p63s1
3s 3p
: Argon (= > /,)
[Ne] 3s23p6
Ne [Ne]3s1
Ne
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he Aubau Principal (cont4)
• We now have the orbital configurations for the first 18 elements.
• Elements in same column have the same # of valence electrons!
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he Aubau Principal (cont4)
• Similar to Sodium, we begin the next row of the periodic table by adding electrons to the 4s orbital.
• Why not 3d before 4s?
• 3d is closer to the nucleus
• 4s allows for closer
approach; therefore, is energetically preferred.
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he Aubau Principal (cont4)
• Elements Z=19 and Z= 20:
Z= 19, Potassium: 1s22s22p63s23p64s1 = [Ar]4s1
Z= 20, Calcuim: 1s22s22p63s23p64s2 = [Ar]4s2
• Elements Z=21to Z=30 have occupied d orbitals:
Z= 21, Scandium: 1s22s22p63s23p64s23d1 = [Ar] 4s23d1
Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10
Z = 24, Chromium: [Ar] 4s13d5 exception
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he Aubau Principal (cont4)
• This orbital filling scheme gives rise to the modern
periodic table.
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he Aubau Principal (cont4)
• After Lanthanum ([Xe]6s25d1), we start filling 4f.
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he Aubau Principal (cont4)
• After Actinium ([Rn]7s26d1), we start filling 5f.
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he Aubau Principal (cont4)
• Heading on column given total number of valence
electrons.
h A b P i i l ( )
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he Aubau Principal (cont4)
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adio atomico
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adio atomico
Potencial de ioni&acion
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Potencial de ioni&acion
(g)
> (g)
C C e- ∆H > DP
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Ai id d El t i
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Ainidad Electronica
(g)
C e- > (g)
- ∆H > EA
Electronegati!it
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%
ulli1en DPCAE+ Pauling
lli1 li
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ulli1en !s Pauling
Electronegati!idad (cont)
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Electronegati!idad (cont)
Atomos pequeGos
Son electronegati!os
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Orbitales Hibridos
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Etileno
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Etileno
Acetileno
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Elementos de teoria de grupos de simetria
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Elementos de simetria molecular
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Character table for D3h point group
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E 2C3 3C'2 σh 2S3 3σv
linear,
rotationsquadratic
A'1 / / / / / / #+C%+ &+
A'2 / / -/ / / -/ &
E' + -/ . + -/ . (# %) (#+-%+ #%)
A''1 / / / -/ -/ -/
A''2 / / -/ -/ -/ / &
E'' + -/ . -+ / . ( # %) (#&%&)
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E C3 3C2 !S" !σd
linear,
rotationsquadratic
A1 / / / / / #+C%+C&+
A2 / / / -/ -/
E + -/ + . .(+&+-#+-%+
#+-%+)
#1 3 . -/ / -/ ( # % &)
#2 3 . -/ -/ / (# % &) (#% #& %&)
Character table for Td point
group
eoria de orbitales moleculares
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eoria de orbitales moleculares
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Hermitian Operator
eoria de orbitales moleculares (cont)
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S>.
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S .
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eoria de Huc1el
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HOO 'O
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FE=AS D<EO'E?'AES
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FESAS D<EO'E?'AESMelting Points and Boiling Points of Similar Substances with Increasing Formula Weights
FW ( / l)
(°)
b (°)
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Substance FW (g/mol) mp (°) bp (°)F
! "# $!!% $&##
l! '& $&%%# $"*+Br
! &+% $'! ,#'#I! !,* &&", &#*",
Melting Points and Boiling Points of Substances with Similar Formula Weights
Substance FW (g/mol) mp (°) bp (°)
F! "# $!!% $&##
-. "% $&+* $&,!
". "! $* +,
a *% #" &*#*
-aF *! " &+,
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FE=AS D<EO'E?'AESdispersion
Iipolo-dipolo
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po o d po o
Puentes de hidrogeno
Don-dipolo
u-momento dipolar
J-carga de ion
Iipolo-dipolo
inducido
FESAS D<EO'E?'AES
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problemas
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?alculate the 2a!elength and requenc% o the photon emitted i an
electron in a onedimensional
bo# o length /.00 nm (1.00×10−9 m) makes a transition from n 3 to
n 2
and the energ% dierence is entirel% con!erted into the energ% o the
photon
Pretend that electrons are bosons 2ith &ero spin4 Iescribe
ho2 the ground state o the helium atom 2ould dier rom
the actual ground state in the orbital appro#imation4
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sp Hybrid Orbitals
F
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Be
BeK
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sp2 and sp3 Hybrid Orbitals$%3
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?H
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H+O
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&%
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"alence Shell Electron Pair epulsion ("SEP) odel
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The bond angles decrease as
the number of nonbonding
electron pairs increases
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Electrons in multiple bonds, like nonbonding electrons, exert a greater
repulsive force on adjacent electron pairs than do single bonds
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(eo)etries of*olecules +ith
Epanded -alence
Shells
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f there is a non!bonding pair of electrons "a #larger# electron cloud$,
it %ill go in the axial position to minimi&e electron repulsion
eoria de Enlaces de "alencia
H+
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O de H+
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eoria de esonancia
Many simple organic compounds, such as methane, ethene,
etc., can be adequately represented by a single Lewis
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etc., can be adequately represented by a single Lewis
structure:
methane - CH4
ethene - H2C=CH
2
eoria de esonancia
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Acidos % Bases
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'r(nsted )cid!'ase Theory
BrLnsted argued that all acid-base reactions in!ol!e the transer o an HC ion or proton4 ;ater reacts2ith itsel or e#ample b% transerring an HC ion rom one molecule to another to orm an H
3OC ion
and an OH- ion4
)cid!*issociation E+uilibrium onstant
Acids are oten di!ided into categories such as MstrongM and M2ea14M One measure o the strength o an
acid is the acid.dissociation equilibriu) constant K a or that acid4
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;hen K a is relati!el% large 2e ha!e a strong acid4
H?l5 K a > / # /.3
;hen it is small 2e ha!e a 2ea1 acid4
?H3
?O+
H5 K a
> /4, # /.-
Dn /@.@ S P ' SLrenson suggested that the enormous range o concentrations o the
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Dn /@.@ S4 P4 '4 SLrenson suggested that the enormous range o concentrations o the
H3OC and OH- ions in aqueous solutions could be compressed into a more manageable
set o data b% ta1ing ad!antage o logarithmic mathematics and calculating the pH or pOH o the solution4
pH > - log NH3OC
pOH > - log NOH-
he MpM in pH and pOH is an operator that indicates that the negati!e o the logarithm
should be calculated or an% quantit% to 2hich it is attached4 hus p7 a is the negati!e
o the logarithm o the acid-dissociation equilibrium constant4
p7 a
> - log K a
he onl% disad!antage o using p7 a as a measure o the relati!e strengths o acids isthe act that large numbers no2 describe 2ea1 acids and small (negati!e) numbers
describe strong acids4
H?l5 p7 a > -3
?H3?O
+H5 p7
a > 40
H+O5 p7
a > /40
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K a K
b > K
2 > / # /.-/
Compound K a pK a Conjugate Base K pK
HD 3 # /.@ -@4 D- 3 # /.-+ +34
H?l / # /.* -* ?l- / # /.-+. +.
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H+SO
/ # /.3 -3 HSO
- / # /.-/0 /0
H3OC -/40 H
+O /4, # /.-/* /40
H<O3 +, -/4 <O
3- 34* # /.-/* /4
H3PO
04/ # /.-3 +4/ H
+PO
- /4 # /.-/+ //4@
?H3?O
+H /4, # /.- 40 ?H
3?O
+- 4* # /.-/. @43
H+S /4. # /.-0 04. HS- / # /.-0 04.
H+O /4, # /.-/* /40 OH- -/40
?H3OH / # /.-/, /, ?H
3O- / # /. -
H? ?H / # /.-+ + H? ?- / # /.// -//
<H3 / # /.-33
33 <H+-
/ # /./@
-/@
H+ / # /.-3 3 H- / # /.+/ -+/
?H+>?H
+ / # /.- ?H
+>?H- / # /.3. -3.
?H / # /.-@ @ ?H
3- / # /.3 -3
/e+is acid5 An electron-pair acceptor such as the HC ion
he pair o electrons that 2ent into the ne2 co!alent bond 2ere donated b% the OH- ion4 'e2is thereore
argued that an% substance that can act as an electron-pair donor is a /e+is base4
/e+is base5 An electron pair donor such as the OH- ion
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/e+is base5 An electron-pair donor such as the OH ion
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+H+O> H3OCCOH-
+<H3> <HC<H+-
+HF> H+F
C
CF
-
+SO+> SO+CCSO3+-
<aOHCNH3O?l> <a?lC+H+O
<a<H+C<H?l> <a?lC+<H3
<aFCNH+F?l> <a?lC+HF
<aFCNH+F?l> <a?lC+HF
<a+SO3CSO?l+> +<a?lC+SO+
eaciones de neutrali&acion
aromaticidad
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Estado Solido
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Solidos uno % bidimencionales
#rans.poliacetileno
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Cis.poliacetileno
calentar
a b
a0b
a-b>
banda de conducion
banda de !alencia
Solidos uno % bidimencionales